# A retroanalysis problem in bridge

This is an entry into the 29th fortnightly topic challenge - Retrograde Analysis.

You're passing a bridge table when one of the players (South) is called away suddenly. He gives you his hand and says "There are no trumps. You need all seven tricks. It's your lead." before disappearing. You find that you're declarer, South, with these hands:

    ♠ K2
♡ Q2
♢ 2
♣ 32

N
W       E
S

♠ A3
♡ AJ
♢ A3
♣ A


The other players refuse to tell you anything about the play of the first six tricks. You lead your aces, and both defenders follow suit.

How do you play the last three tricks?

This problem is a variation, by me, of one by Jonathan Mestel.

• Thanks for participating in the challenge, we need a few more seeing as this is only the second – Beastly Gerbil Apr 1 '17 at 7:49

6 rounds have been played and no-one has any voids before you sit down. There are therefore at most 1 round of spades and hearts (if there were 2 then 8 cards are played + 4 visible + 2 with the opponents =14), and 2 rounds of diamonds and clubs.

The only way to get to 6 is if exactly those were played, meaning that before you sat down there had been 1 round of spades and hearts and 2 of diamonds and clubs.

Of course, you had no way of knowing that until you played your aces, which was therefore grotesquely irresponsible, but we will leave that aside for now.

The point is that your opponents are now void in diamonds and clubs. We assume the King of hearts is still out.

So: